1. The problem states that the graph of $g(x)$ is a translation of $f(x) = |x|$. 2. The general form for a translated absolute value function is $$g(x) = a|x - h| + k$$ where: - $a$ controls the vertical stretch or compression and reflection. - $h$ controls the horizontal shift. - $k$ controls the vertical shift. 3. The given graph has a vertex at $(0, 6)$ and opens upward, which means: - The vertex form is $g(x) = a|x - 0| + 6 = a|x| + 6$. - Since the graph opens upward and looks like the original $|x|$ shape, $a = 1$. 4. Therefore, the function rule for $g(x)$ is: $$g(x) = 1|x| + 6 = |x| + 6$$ 5. This matches the given function rule and the vertex position. Final answer: $$g(x) = |x| + 6$$